The decomposition of 3-dimensional Poincaré complexes
J. CrispUniversité de Bourgogne, Dijon, France
We show that if the fundamental group of an orientable PD3-complex has infinitely many ends then it is either a proper free product or virtually free of finite rank. It follows that every PD3-complex is finitely covered by one which is homotopy equivalent to a connected sum of aspherical PD3-complexes and copies of . Furthermore, it is shown that any torsion element of the fundamental group of an orientable PD3-complex has finite centraliser.
Cite this article
J. Crisp, The decomposition of 3-dimensional Poincaré complexes. Comment. Math. Helv. 75 (2000), no. 2, pp. 232–246DOI 10.1007/PL00000372